Identifier
Mp00018: left border symmetryBinary trees
Mp00017: to 312-avoiding permutationPermutations
Mp00151: Permutations to cycle type
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0009;cc-rep-3
[.,.]=>[.,.]=>[1]=>{{1}} [.,[.,.]]=>[.,[.,.]]=>[2,1]=>{{1,2}} [[.,.],.]=>[[.,.],.]=>[1,2]=>{{1},{2}} [.,[.,[.,.]]]=>[.,[.,[.,.]]]=>[3,2,1]=>{{1,3},{2}} [.,[[.,.],.]]=>[.,[[.,.],.]]=>[2,3,1]=>{{1,2,3}} [[.,.],[.,.]]=>[[.,[.,.]],.]=>[2,1,3]=>{{1,2},{3}} [[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,3,2]=>{{1},{2,3}} [[[.,.],.],.]=>[[[.,.],.],.]=>[1,2,3]=>{{1},{2},{3}} [.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>{{1,4},{2,3}} [.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>{{1,2,3,4}} [.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>{{1,3,4},{2}} [.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>{{1,2,4},{3}} [.,[[[.,.],.],.]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>{{1,2,3,4}} [[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>{{1,3},{2},{4}} [[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>{{1,2,3},{4}} [[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>{{1,2},{3,4}} [[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>{{1,2},{3},{4}} [[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>{{1},{2,4},{3}} [[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>{{1},{2,3,4}} [[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>{{1},{2,3},{4}} [[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>{{1},{2},{3,4}} [[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>{{1},{2},{3},{4}} [.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}} [.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>{{1,2,4,5},{3}} [.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>{{1,2,3,4,5}} [.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>{{1,2,3,4,5}} [.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>{{1,3,5},{2,4}} [.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>{{1,2,3,4,5}} [.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}} [.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>{{1,2,5},{3,4}} [.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>{{1,2,3,4,5}} [.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>{{1,2,4,5},{3}} [.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>{{1,2,3,5},{4}} [.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}} [[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>{{1,2,3,4},{5}} [[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}} [[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}} [[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>{{1,2,3},{4,5}} [[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}} [[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}} [[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>{{1,2},{3,4,5}} [[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}} [[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}} [[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}} [[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>{{1},{2,3,4,5}} [[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}} [[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}} [[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>{{1},{2,3,4,5}} [[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}} [[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}} [[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}} [[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}} [[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}} [[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}} [[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}} [[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}} [.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}} [.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}} [.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>{{1,2,3,4,5,6}} [.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}} [.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}} [.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}} [.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>{{1,2,3,4,5,6}} [.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}} [.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>{{1,2,3,5,6},{4}} [.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}} [.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}} [.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}} [.,[.,[[[[.,.],.],.],.]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}} [.,[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}} [.,[[.,.],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}} [.,[[.,.],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}} [.,[[.,.],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>{{1,2,3,4,5,6}} [.,[[.,.],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}} [.,[[.,[.,.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}} [.,[[.,[.,.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>{{1,2,3,4,6},{5}} [.,[[[.,.],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [.,[[[.,.],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}} [.,[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}} [.,[[.,[[.,.],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>{{1,3,4,5,6},{2}} [.,[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}} [.,[[[.,[.,.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}} [.,[[[[.,.],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [.,[[.,[.,[.,[.,.]]]],.]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}} [.,[[.,[.,[[.,.],.]]],.]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>{{1,2,3,5,6},{4}} [.,[[.,[[.,.],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>{{1,2,3,4,5,6}} [.,[[.,[[.,[.,.]],.]],.]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>{{1,2,3,4,5,6}} [.,[[.,[[[.,.],.],.]],.]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}} [.,[[[.,.],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}} [.,[[[.,.],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>{{1,2,3,4,5,6}} [.,[[[.,[.,.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}} [.,[[[[.,.],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}} [.,[[[.,[.,[.,.]]],.],.]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}} [.,[[[.,[[.,.],.]],.],.]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>{{1,2,3,4,5,6}} [.,[[[[.,.],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}} [.,[[[[.,[.,.]],.],.],.]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}} [.,[[[[[.,.],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}} [[.,.],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}} [[.,.],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}} [[.,.],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>{{1,2,3,4,5},{6}} [[.,.],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}} [[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}} [[.,.],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}} [[.,.],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [[.,.],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}} [[.,.],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}} [[.,.],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}} [[.,.],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}} [[.,.],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [[.,[.,.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}} [[.,[.,.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>{{1,2,3,4},{5,6}} [[.,[.,.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}} [[.,[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}} 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[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,10,3]=>{{1,2},{3,4,5,6,7,9,10},{8}} [[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,10,3]=>{{1,2},{3,5,7,9,10},{4},{6},{8}} [[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,8,7,9,6,10,5]=>{{1,3,4},{2},{5,6,7,8,9,10}} [[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,10,5]=>{{1,3,4},{2},{5,7,9,10},{6},{8}} [[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,8,7,9,6,10,5]=>{{1,2},{3,4},{5,6,7,8,9,10}} [[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,10,5]=>{{1,2},{3,4},{5,7,9,10},{6},{8}} [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,9,8,10,7]=>{{1,2,3,4,5,6},{7,9,10},{8}} [[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,9,8,10,7]=>{{1,3,5,6},{2},{4},{7,9,10},{8}} [[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,9,8,10,7]=>{{1,2},{3,5,6},{4},{7,9,10},{8}} [[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,9,8,10,7]=>{{1,3,4},{2},{5,6},{7,9,10},{8}} [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,9,8,10,7]=>{{1,2},{3,4},{5,6},{7,9,10},{8}} [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9]=>{{1,5,7,8},{2,3,4,6},{9,10}} [[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9]=>{{1,4,5,7,8},{2,3,6},{9,10}} [[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9]=>{{1,3,4,5,6,7,8},{2},{9,10}} [[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}} [[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9]=>{{1,2,3,4,5,6},{7,8},{9,10}} [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9]=>{{1,3,5,6},{2},{4},{7,8},{9,10}} [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9]=>{{1,2},{3,5,6},{4},{7,8},{9,10}} [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9]=>{{1,3,4},{2},{5,6},{7,8},{9,10}} [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}} [.,[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]]=>[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>{{1,2,4,5,6,7,9,10,11,12},{3,8}} [.,[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]]=>[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>{{1,5,9,11,12},{2,4,7,10},{3,8},{6}} [.,[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]]=>[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}} [.,[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]]=>[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>{{1,5,9,11,12},{2,3,4,6,7,8,10}} [.,[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]]=>[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}} [.,[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]]=>[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>{{1,4,5,6,8,9,11,12},{2,3,7,10}} [.,[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]]=>[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>{{1,5,9,11,12},{2,3,4,6,7,8,10}} [.,[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]]=>[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>{{1,4,5,9,11,12},{2,3,6,7,8,10}} [.,[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]]=>[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>{{1,2,3,5,6,7,8,9,10,11,12},{4}} [.,[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]]=>[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>{{1,5,8,9,11,12},{2,3,4,6,7,10}} [.,[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]]=>[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>{{1,4,5,6,8,9,11,12},{2,3,7,10}} [.,[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]]=>[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>{{1,5,8,9,11,12},{2,3,4,6,7,10}} [.,[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]]=>[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>{{1,4,5,8,9,11,12},{2,3,6,7,10}} [.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]]=>[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>{{1,3,5,8,9,11,12},{2},{4,7,10},{6}} [.,[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]]]=>[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}} [.,[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}} [.,[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]]=>[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}} [.,[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}} 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[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}} [.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>{{1,2,3,4,5,7,8,9,10,11,12},{6}} [.,[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>{{1,3,5,7,8,9,10,11,12},{2},{4},{6}} [.,[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>{{1,3,6,7,9,11,12},{2,5,8},{4},{10}} [.,[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}} [.,[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}} [.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>{{1,2,3,4,5,6,7,8,9,11,12},{10}} [.,[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>{{1,3,7,9,11,12},{2},{4,5,6,8},{10}} [.,[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>{{1,5,7,9,11,12},{2,3,4,6},{8},{10}} [[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>{{1,2},{3,5,8,9,11,12},{4,7,10},{6}} [[.,[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}} [[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}} [[.,[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}} [[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}} [[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>{{1,2},{3,5,9,11,12},{4},{6,7,8,10}} [[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>{{1,2},{3,5,8,9,11,12},{4},{6,7,10}} [[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>{{1,2},{3,4,5,6,7,8,9,10,11,12}} [[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>{{1,2},{3,5,7,8,9,10,11,12},{4},{6}} [[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>{{1,2},{3,7,9,11,12},{4,5,6,8},{10}} [[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>{{1,2},{3,6,7,9,11,12},{4,5,8},{10}} [[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>{{1,2},{3,5,6,7,8,9,11,12},{4},{10}} [[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>{{1,2},{3,4,5,6,7,9,11,12},{8},{10}} [[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>{{1,2},{3,5,7,9,11,12},{4},{6},{8},{10}} [[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>{{1,3,4},{2},{5,9,11,12},{6,7,8,10}} [[.,[[.,.],[[[.,.],[.,.]],[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>{{1,3,4},{2},{5,8,9,11,12},{6,7,10}} [[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>{{1,3,4},{2},{5,7,8,9,10,11,12},{6}} [[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>{{1,3,4},{2},{5,6,7,8,9,11,12},{10}} [[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>{{1,3,4},{2},{5,7,9,11,12},{6},{8},{10}} [[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>{{1,2},{3,4},{5,9,11,12},{6,7,8,10}} [[[.,[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>{{1,2},{3,4},{5,8,9,11,12},{6,7,10}} [[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>{{1,2},{3,4},{5,7,8,9,10,11,12},{6}} [[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>{{1,2},{3,4},{5,6,7,8,9,11,12},{10}} [[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>{{1,2},{3,4},{5,7,9,11,12},{6},{8},{10}} [[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>{{1,2,3,4,5,6},{7,8,9,10,11,12}} [[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>{{1,2,3,4,5,6},{7,9,11,12},{8},{10}} [[.,[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>{{1,3,5,6},{2},{4},{7,8,9,10,11,12}} [[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>{{1,3,5,6},{2},{4},{7,9,11,12},{8},{10}} [[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>{{1,2},{3,5,6},{4},{7,8,9,10,11,12}} [[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>{{1,2},{3,5,6},{4},{7,9,11,12},{8},{10}} [[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>{{1,3,4},{2},{5,6},{7,8,9,10,11,12}} [[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>{{1,3,4},{2},{5,6},{7,9,11,12},{8},{10}} [[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>{{1,2},{3,4},{5,6},{7,8,9,10,11,12}} [[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>{{1,2},{3,4},{5,6},{7,9,11,12},{8},{10}} [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>{{1,5,7,8},{2,3,4,6},{9,11,12},{10}} [[.,[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>{{1,4,5,7,8},{2,3,6},{9,11,12},{10}} [[.,[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>{{1,3,4,5,6,7,8},{2},{9,11,12},{10}} [[.,[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>{{1,3,5,7,8},{2},{4},{6},{9,11,12},{10}} [[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>{{1,2},{3,4,5,6,7,8},{9,11,12},{10}} [[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>{{1,2},{3,5,7,8},{4},{6},{9,11,12},{10}} [[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>{{1,3,4},{2},{5,7,8},{6},{9,11,12},{10}} [[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>{{1,2},{3,4},{5,7,8},{6},{9,11,12},{10}} [[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>{{1,2,3,4,5,6},{7,8},{9,11,12},{10}} [[[.,[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>{{1,3,5,6},{2},{4},{7,8},{9,11,12},{10}} [[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>{{1,2},{3,5,6},{4},{7,8},{9,11,12},{10}} [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>{{1,3,4},{2},{5,6},{7,8},{9,11,12},{10}} [[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>{{1,2},{3,4},{5,6},{7,8},{9,11,12},{10}} [[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>{{1,3,6,7,9,10},{2,5,8},{4},{11,12}} [[.,[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}} [[.,[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}} [[.,[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}} [[.,[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}} [[.,[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>{{1,3,7,9,10},{2},{4,5,6,8},{11,12}} [[.,[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>{{1,3,6,7,9,10},{2},{4,5,8},{11,12}} [[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>{{1,2,3,4,5,6,7,8,9,10},{11,12}} [[.,[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>{{1,3,5,6,7,8,9,10},{2},{4},{11,12}} [[.,[.,.]],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>{{1,5,7,9,10},{2,3,4,6},{8},{11,12}} [[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>{{1,2},{3,7,9,10},{4,5,6,8},{11,12}} [[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>{{1,2},{3,6,7,9,10},{4,5,8},{11,12}} [[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]=>[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>{{1,2},{3,5,6,7,8,9,10},{4},{11,12}} [[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>{{1,2},{3,4,5,6,7,9,10},{8},{11,12}} [[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>{{1,3,4},{2},{5,6,7,8,9,10},{11,12}} [[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>{{1,2},{3,4},{5,6,7,8,9,10},{11,12}} [[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>{{1,2,3,4,5,6},{7,9,10},{8},{11,12}} [[[.,[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>{{1,5,7,8},{2,3,4,6},{9,10},{11,12}} [[[.,[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>{{1,4,5,7,8},{2,3,6},{9,10},{11,12}} [[[.,[.,.]],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>{{1,3,4,5,6,7,8},{2},{9,10},{11,12}} [[[.,[.,.]],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>{{1,3,5,7,8},{2},{4},{6},{9,10},{11,12}} [[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>{{1,2},{3,4,5,6,7,8},{9,10},{11,12}} 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[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>{{1,5},{2,4},{3},{6},{7},{8},{9},{10}} [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>{{1,6},{2,5},{3,4},{7},{8},{9},{10}} [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>{{1,7},{2,6},{3,5},{4},{8},{9},{10}} [[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>{{1,2,6,7},{3,5},{4},{8},{9}} [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}} [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>{{1,7,8},{2,6},{3,5},{4},{9}} [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[6,5,8,7,4,3,2,1,9]=>{{1,3,6,8},{2,4,5,7},{9}} [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>{{1,7,9},{2,6},{3,5},{4},{8}} [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>{{1,8,9},{2,7},{3,6},{4,5},{10}} [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]=>{{1,5},{2,4},{3},{6,8},{7},{9}} [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]=>{{1,7},{2,6},{3,5},{4},{8,9},{10}} [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>{{1,2,7,8,9},{3,6},{4,5}} [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>{{1,2,10,11},{3,9},{4,8},{5,7},{6}} [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[2,8,9,7,6,5,4,3,1]=>{{1,2,3,8,9},{4,7},{5,6}} [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[2,8,7,9,6,5,4,3,1]=>{{1,2,3,4,7,8,9},{5,6}} [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}} [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[4,5,3,2,1,9,8,7,6]=>{{1,2,4,5},{3},{6,9},{7,8}} [[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9,10}} [[[[[[[.,.],.],.],.],.],[[.,.],.]],.]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}} [[[[[[.,.],.],.],.],[[[.,.],.],.]],.]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[1,3,4,5,2,6,7,8,9]=>{{1},{2,3,4,5},{6},{7},{8},{9}} [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>{{1},{2,4},{3},{5},{6},{7},{8},{9}} [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}} [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>{{1,7,8,9},{2,6},{3,5},{4}} [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>{{1,2,8},{3,7},{4,6},{5},{9}} [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>{{1,2},{3,4,5,6,7,8,9}} [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,4,5,6,7,8,3,9,2]=>{{1},{2,4,6,8,9},{3,5,7}} [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10,11]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}} [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2,3}} [.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[5,4,3,2,6,7,8,9,1]=>{{1,5,6,7,8,9},{2,4},{3}} [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>{{1,2,5,6},{3,4},{7},{8},{9},{10}} [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[2,1,3,5,6,7,8,9,4]=>{{1,2},{3},{4,5,6,7,8,9}} [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]=>[6,5,7,8,4,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}} [[.,.],[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.]=>[6,5,4,7,8,3,2,1,9]=>{{1,2,3,4,5,6,7,8},{9}} [[.,.],[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>{{1,6,7,8},{2,5},{3,4},{9}} [[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[7,6,8,9,5,4,3,2,1,10]=>{{1,2,3,4,6,7,8,9},{5},{10}} [[.,.],[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]=>[7,6,5,8,9,4,3,2,1,10]=>{{1,3,5,7,9},{2,4,6,8},{10}} [[.,.],[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]=>[7,6,5,4,3,8,9,2,1,10]=>{{1,7,9},{2,6,8},{3,5},{4},{10}} [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[7,6,5,4,3,2,8,9,1,10]=>{{1,7,8,9},{2,6},{3,5},{4},{10}} [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>{{1,2,3,4},{5,9},{6,8},{7}} [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[1,9,8,10,7,6,5,4,3,2]=>{{1},{2,3,4,8,9,10},{5,7},{6}} [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[8,7,6,5,4,3,2,10,9,1]=>{{1,8,10},{2,7},{3,6},{4,5},{9}} [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>{{1,2,3,9,10,11},{4,8},{5,7},{6}} [[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}} [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9,10]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}} [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]=>[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>{{1,2},{3,4,5},{6},{7},{8},{9}} [[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>{{1,2,3,4,5},{6},{7},{8},{9}} [[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[2,3,1,5,4,6,7,8,9]=>{{1,2,3},{4,5},{6},{7},{8},{9}} [[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>{{1},{2,3},{4,5},{6},{7},{8},{9}} [[[[[[[.,.],.],.],.],[[.,.],.]],.],.]=>[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>{{1},{2},{3,4,5},{6},{7},{8},{9}} [.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>{{1,6,7,8,9},{2,5},{3,4}} [[[.,[[[.,.],.],[[[.,.],.],.]]],.],.]=>[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[1,2,5,6,7,4,8,9,3]=>{{1},{2},{3,5,7,8,9},{4,6}}
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].